Quantum solution for the one-dimensional Coulomb problem

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.064101· OSTI ID:21550229

Nunez-Yepez, H N; Salas-Brito, A L; Solis, Didier A ^[1]

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1. Departamento de Fisica, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Apartado Postal 55-534, Iztapalapa CP 09340 D. F. (Mexico)

The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.

• OSTI ID: 21550229
• Journal Information: Physical Review. A, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevA.83.064101; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
BINDING ENERGY
COULOMB FIELD
EIGENFUNCTIONS
EIGENSTATES
HYDROGEN
MATHEMATICAL SOLUTIONS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM MECHANICS
SINGULARITY
SUPERSELECTION RULES
SUPERSYMMETRY
ELECTRIC FIELDS
ELEMENTS
ENERGY
FUNCTIONS
MECHANICS
NONMETALS
SELECTION RULES
SYMMETRY